Inappettance - not eating - can make glucose control tricky.
If you are home testing, you can take the data you have and see how much drop you get when both eating and giving insulin.
When not eating, and the glucose is high, some insulin is going to be helpful to reduce the glucose. The trick is figuring out how much. In a hospital setting, they'd put Humulin or Novolin R in an IV drip and titrate the dose as needed and that may be the best place for her right now.
When you are home testing, you can test a token dose and see what happens. Since you're at 3-4 units, a token dose of 0.5 to 1 unit with nadir monitoring may help. Yes, you must be careful as you don't want to give too much. This will be data collection which you can use when/if the situation happens again.
Figuring out why the cat isn't eating is going to be critical. Gagging makes me wonder about some sort of throat obstruction blocking swallowing. And it may be necessary to insert a feeding tube to help her eat until she can stabilize.